Question

You used a telescope and other mathematics to discover that Jupiter is 5.20 au from the sun. Use the equation to find its orbital period. rounded to the nearest tenths

Answer 1

(period squared) / (distance cubed) is the same number for every object in orbit around the sun. (Kepler's third law). For the Earth, it's (1yr)^2/(1AU)^3=1 . For Jupiter, it's (5.2)^(3/2) which is 11.85 years.
It would have been easier and more awesome if you used your eyes to observe Jupiter in the sky for a long long time, and noticed that it takes 11.85 years to come back to the same place among the stars, and THEN used Kepler's third law to calculate that Jupiter must be 5.2 times as far from the sun as WE are.

Answer 2

Answer:

11.9 years

Explanation:

We can find the orbital period by using Kepler's third law, which states that the ratio between the square of the orbital period and the cube of the average distance of a planet from the Sun is constant for every planet orbiting aroudn the Sun:

$\frac{T^2}{r^3}=const.$

Using the Earth as reference, we can re-write the law as

$\frac{T_e^2}{r_e^2}=\frac{T_j^2}{r_j^3}$

where

Te = 1 year is the orbital period of the Earth

re = 1 AU is the average distance of the Earth from the Sun

Tj = ? is the orbital period of Jupiter

rj = 5.20 AU is the average distance of Jupiter from the Sun

Substituting the numbers and re-arranging the equation, we find:

$T_j=\sqrt{\frac{T_e^2 r_j^3}{T_j^2}}=\sqrt{\frac{(1 y)^2 (5.2 AU)^3}{(1 AU)^3}}=11.9 y$